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1、IntroductiontotheTheoryofNonhnearOptimizationJohannesJahnIntroductiontotheTheoryofNonHnearOptimizationThirdEditionWith31FiguresSpringerProf.Dr.JohannesJahnUniversitatErlangen-NiirnbergInstitutfurAngewandteMathematikMartensstr.391058ErlangenGermanyjahn@am.uni-erlangen.deLibraryofCongressCont
2、rolNumber:2006938674ISBN978-3-540-49378-5SpringerBerlinHeidelbergNewYorkISBN978-3-540-61407-4SecondEditionSpringerBerlinHeidelbergNewYorkThisworkissubjecttocopyright.Allrightsarereserved,whetherthewholeorpartofthematerialisconcerned,specificallytherightsoftranslation,reprinting,reuseofillus
3、trations,recitation,broad•casting,reproductiononmicrofilmorinanyotherway,andstorageindatabanks.DuplicationofthispublicationorpartsthereofispermittedonlyundertheprovisionsoftheGermanCopyrightLawofSeptember9,1965,initscurrentversion,andpermissionforusemustalwaysbeobtainedfromSpringer.Violatio
4、nsareliabletoprosecutionundertheGermanCopyrightLaw.SpringerispartofSpringerScience+BusinessMediaspringer.com©Springer-VerlagBerlinHeidelberg1994,1996,2007Theuseofgeneraldescriptivenames,registerednames,trademarks,etc.inthispublicationdoesnotimply,evenintheabsenceofaspecificstatement,thatsuc
5、hnamesareexemptfromtherelevantprotectivelawsandregulationsandthereforefreeforgeneraluse.Production:LE-TgXJelonek,Schmidt&VocklerGbR,LeipzigCover-design:ErichKirchner,HeidelbergSPIN1193204842/3100YL-543210Printedonacid-freepaperToClaudiaandMartinPrefaceThisbookpresentsanapplication-orientedi
6、ntroductiontothethe•oryofnonhnearoptimization.Itdescribesbasicnotionsandconcep•tionsofoptimizationinthesettingofnormedorevenBanachspaces.VarioustheoremsareappHedtoproblemsinrelatedmathematicalareas.Forinstance,theEuler-Lagrangeequationinthecalculusofvariations,thegenerahzedKolmogorovconditi
7、onandthealternationtheoreminapproximationtheoryaswellasthePontryaginmaximumprincipleinoptimalcontroltheoryarederivedfromgeneralresultsofoptimization.Becauseoftheintroductorycharacterofthistextitisnotintendedtogiveacompletedescriptionofallapproachesinopti
